The present invention relates generally to signal reconstruction systems and methods, and more particularly, to an improved linear signal reconstruction system and method that employs differentiation of digitized signals followed by linear digital to analog conversion and followed by integration thereof to provide for a more accurate reproduction of an original analog signal.
The reconstruction of analog waveforms from digital representations is an important technology. The most common forms of this reconstruction uses multi-bit digital to analog converters. This techniques has inherent limitations. These limitations include linearity, switching noise (particularly at zero), image rejection at multiples of the sampling frequency, voltage accuracy, phase accuracy, and bandwidth restrictions. These limitations affect system performance and usually result in design trade-offs.
More specifically, the stair-case approximation technique is a traditional digital to analog conversion technique. However, its error function contains the fundamental frequency at a 90 degree phase shift from the original signal plus aliased harmonics. This phase shifted signal varies in amplitude as a function of point density and causes the reconstructed signal to be reduced in amplitude and shifted in phase. Furthermore, spectral analysis of the stair-case approximation show that sampling images are replicated at multiples of the sampling frequencies (aliased harmonics). The magnitude of these images vary as a function of the number of points used to generate the desired baseband signal. That is, the magnitude of the out-of-band images increase as a function of decreasing point density.
Another disadvantage with the stair-case approximation technique is that it introduces a phase lag into the reproduced signal. This phase lag occurs due to the sample-and-hold scheme that is employed. The amount of phase lag introduced by the stair-case approximation is proportional to the number of points used to generate the desired signal. Larger point densities generate smaller phase lag errors.
A fundamental is present in the stair-case approximation technique. Mathematically incorporating this fundamental into a base band signal (subtracting it) results in a signal whose amplitude was less than that of the original signal. This is an undesired amplitude error.